Export select pieces of a model?
After selecting the objects you want, go to File -> Export. In the bottom left corner, you'll see a panel labeled "Export [name of file type]". There, you can click a checkbox labeled either "Selected Objects" or "Selected Only". The .ply, .stl, and .bvh files don't have these options. For example, here's the "Selected Objects" checkbox when you export to .fbx.